Towards an adequate definition of distribution for first-order logic (Q1346217)

The paper defends the traditional syllogistic notion of distribution against the attacks of Geach. A monadic predicate, \(F\), is taken to be distributed in the sentence \(A\) iff for some formula of one free variable, \(x\), not containing \(F\), \(A \vdash \forall x (Fx \supset B)\) but \(A \not \vdash \forall xB\). This definition is shown to satisfy a list of desiderata including the traditional law of distribution: in a valid syllogistic argument any predicate distributed in the conclusion is distributed in at least one premise. To find a definition of validity satisfying the same criteria, but extending the law to all inferences in first-order logic is left as an open problem.